[Solution] Chopping Carrots (Hard Version) Codeforces Solution

D2. Chopping Carrots (Hard Version)

time limit per test

4 seconds

memory limit per test

64 megabytes

input

standard input

output

standard output

This is the hard version of the problem. The only difference between the versions is the constraints on n$n$, k$k$, ai$a_i$, and the sum of n$n$ over all test cases. You can make hacks only if both versions of the problem are solved.

Note the unusual memory limit.

You are given an array of integers a1,a2,…,an$a_1,a_2,\dots ,a_n$ of length n$n$, and an integer k$k$.

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The cost of 

Input

The first line contains a single integer t$t$ (1≤t≤100$1\le t\le 100$) — the number of test cases.

The first line of each test case contains two integers n$n$ and k$k$ (1≤n,k≤105$1\le n,k\le {10}^5$).

The second line

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Chopping Carrots (Hard Version) Codeforces Solution

 contains n$n$ integers a1,a2,…,an$a_1,a_2,\dots ,a_n$ (1≤a1≤a2≤…≤an≤105$1\le a_1\le a_2\le \dots \le a_n\le {10}^5$).

It is guaranteed that the sum of n$n$ over all test cases does not exceed 105${10}^5$.

Output

For each test case, print a single integer — the minimum possible cost of an array p$p$ satisfying the condition above.